C.

1
Using the WSA Model to Connect the Solar Wind
Observed Near Earth with its Sources Back at Sun

• C. Nick Arge
• Space Vehicles Directorate/Air Force Research
  Laboratory

SHINE Workshop Aug. 1, 2007
2
Using MHD Simple Solar Wind Models to Trace the
Solar Wind Advantages Disadvantages

• MHD Models
• Advantages
• Rigorous physical foundation.
• Provide 3D global solutions of the key plasma
  parameters (?, T, vector B and V).
• Disadvantages
• Can take many hours to complete single run (even
  at low resolution).
• Require all key plasma parameters be specified at
  their inner boundary.
• Only B reliably known (?).
• Simple Models (such as WSA)
• Disadvantages
• Lack sophisticated physics of MHD models.
• Only predicts radial solar wind speed and IMF
  polarity at L1.
• Advantages
• Run quickly (can simulate entire solar cycles
  worth of predictions in hours).
• ? Allows it to be highly tuned over entire solar
  cycle.
• Highly Validated (Owens et al, 2005 Arge et
  al., 2002)

3
Potential Field Source Surface (PFSS) Coronal
Solution
MODEL OUTPUT
MODEL INPUT Observed Photospheric Field
Source Surface or Coronal Field (2.5 R?)
Source Surface
fs (R?/Rss)2BP(R?)/BP(Rss)
MODEL OUTPUT
Derived Coronal Holes (1.0 R?)
Predicted Solar Wind Speed (2.5 R?)
Closed Field Footpoint
Open Field Footpoint
V fs-n
MODEL OUTPUT
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Traditional Approach for Tracing Field Lines Back
to the Sun

• Traditional approach for tracing the solar wind
  back to the Sun using the PFSS model.
• Follow the field back along the Parker Spiral
  assuming
• Constant (radial) flow speed (as measured
  in-situ) neglecting stream interactions.
• Negligible flow in the latitudinal direction.
• Upon reaching the source surface, the field is
  traced down to the surface using the PFSS model

5
Traditional Approach for Tracing Field Lines Back
to the Sun
f
Vr
B
6
Limitations of the Traditional Field Line
Tracing Approach

• While the traditional approach for tracing the
  solar wind back to the Sun can often yield
  reasonable results,
• Stream interactions can lead to differences up to
  20 in longitude in the mapping compared to
  those done using MHD!! (see Pizzo et al.,1981or
  Riley et al. 1999).
• Assuming field and flow is radial beyond the
  source surface is problematic.
• Magnetic field can still have significant
  displacements there.
• (e.g., Schatten et al. 1971, Zhao and Hoeksema
  1994, Smith et al. 2003)
• One of the reasons for the development of current
  sheet models, which apply beyond the source
  surface. (e.g., Schatten 1971 Zhao et al.
  1992)
• By 5 Rs the field is much more uniform and
  radial and thus concerns over latitudinal
  displacements are mitigated significantly.

7
WSA Model Predictions Observations CR2028
Observed Predicted IMF Polarity
Solar Wind Source Region
Observed Predicted Solar Wind Speed
Solar Wind Source Region
Time
8
WSA Model Predictions Observations CR1896
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PFSSSchatten Current Sheet Model
Outer Coronal Boundary
Schatten Current Sheet Model
PFSS Model
Solar Wind Model (e.g., 1D Kinematic model,
ENLIL, HAF) (5-30Rs to 1AU)
5-30 Rs
2.5 Rs
Source Surface
Plot courtesy of Sarah McGregor
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Outer Coronal Boundary
5 Rs
Sun-Earth Line
2.5 Rs
Source Surface
Plot courtesy of Sarah McGregor
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Using the WSA Model to Trace Solar Wind

• WSA coronal-solar wind model
• Accounts for stream interactions as it transports
  solar wind out into the heliosphere
• Begins transport of the wind beyond the point
  where the flow is primarily radial,
• ? Two major problems associated with simple
  ballistic field line tracing methods overcome
  (without having to resort to an advanced MHD
  model).
• WSA tracks field opposite to that of traditional
  approach
• Wind traced from outer coronal boundary using a
  1-d kinematic model out to 1AU
• Effects due to stream interactions included.
• Keeps track of the individual solar wind parcels
  as they travel out to L1
• ? Simple to associate solar wind predicted at
  Earth with its sources back at Sun
• When model correctly predicts the observed solar
  wind speed and IMF polarity at L1
• ? relatively high confidence that it is
  correctly associating the wind observed at Earth
  with its sources back at Sun.

12
Next Step in Sophistication Use WSA
Coronal-ENLIL MHD Solar Wind Coupled Model
Output of WSA MODEL (R 21.5 R?)
ENLIL 3D MHD Solar Wind Model
Coronal Field Strength
Solar Wind Speed
Output of ENLIL MODEL at 1AU
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Summary

• Traditional simple approach for tracing field
  lines back to the Sun can result in mapping
  errors up to 20 in longitude due to methods two
  major simplifying assumptions
• Constant solar wind speed (no stream
  interactions)
• That the field is radial (immediately) beyond the
  source surface
• The WSA model
• Overcomes (to a large extent) the 2 major
  problems listed above without having to resort to
  MHD.
• Highly tuned and validated (over solar cycle).
• Runs quickly.
• Allows one to rapidly identify the sources of the
  solar wind over the entire cycle.
• Permits one to select periods of interest that
  can be investigated in more detail using more
  advanced methods, if required, such as hybrid
  models (WSA-ENLIL) or FULL MHD.

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Model Output
Model Input
km s-1
Where fs Magnetic field expansion
factor. ?b Minimum angular distance that an
open field footpoint lies from nearest coronal
hole boundary (i.e., Angular depth inside a
coronal hole)
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Potential Field Source Surface (PFSS) Model of
the Corona
Required because coronal magnetic fields are too
weak to measure directly.
j 0
Schatten, Cosmic Electrodynamics, 2, 232, 1971.